Tags: #todo #todo/stub Refs: ?
ideal class group
For orders 
## Exercises
- Show that a DVR \(R\) with a uniformizer has \({ \operatorname{cl}} (R) \cong {\mathbb{Z}}\).
-
Show that a Dedekind domain \(R\) is a UFD iff \({ \operatorname{cl}} (R) = 1\).
- Show that if \(R\) is an integrally closed Noetherian domain then \({ \operatorname{cl}} (R) = 1\) when \(R\) is a UFD.
- Show that the converse holds if \({ \operatorname{cl}} (R)\) is replaced with the divisor class group.
- Show that the ideal class group and divisor class group coincide for DVRs
